In layered semiconductors with spin-orbit interaction (SOI) a persistent spin helix (PSH) state with suppressed spin relaxation is expected if the strengths of the Rashba and Dresselhaus SOI terms, α and β, are equal. Here we demonstrate gate control and detection of the PSH in two-dimensional electron systems with strong SOI including terms cubic in momentum. We consider strain-free InGaAs/InAlAs quantum wells and first determine a ratio α/β 1 for nongated structures by measuring the spin-galvanic and circular photogalvanic effects. Upon gate tuning the Rashba SOI strength in a complementary magnetotransport experiment, we monitor the complete crossover from weak antilocalization via weak localization to weak antilocalization, where the emergence of weak localization reflects a PSH-type state. A corresponding numerical analysis reveals that such a PSH-type state indeed prevails even in presence of strong cubic SOI, however no longer at α = β. An electron moving in an electric field experiences, in its rest frame, an effective magnetic field pointing perpendicularly to its momentum. The coupling of the electron's spin to this magnetic field is known as spin-orbit interaction (SOI). The ability to control the corresponding magnetic field, and thereby spin states, all electrically in gated semiconductor heterostructures 1,2 is a major prerequisite and motivation for research towards future semiconductor spintronics. However, on the downside, the momentum changes of an electron moving through a semiconductor cause sudden changes in the magnetic field leading to spin randomization. Hence, suppression of spin relaxation in the presence of strong, tunable SOI is a major challenge of semiconductor spintronics.In III-V semiconductor heterostructures two different types of SOI exist: (i) Rashba SOI, 3 originating from structure inversion asymmetry (SIA), is linear in momentum k with a strength α that can be controlled by an electric gate.(ii) Dresselhaus SOI 4 is due to bulk inversion asymmetry (BIA), which gives rise to a band spin splitting, given by k-linear and k-cubic contributions. 5 The strength of the linear in k term β = γ k 2 z (where γ is a material parameter) can hardly be changed as it stems from crystal fields. These various spin-orbit terms in layered semiconductors are described by the Hamiltonian H SO = H R + H D with Rashba and Dresselhaus termswith σ x ,σ y the Pauli spin matrices. 7 If the k-cubic terms can be neglected, a special situation emerges if Rashba and Dresselhaus SOI are of equal strength: α = ±β.Then spin relaxation is suppressed. 8,9 A collinear alignment of Rashba and Dresselhaus effective magnetic fields gives rise to spin precession around a fixed axis, leading to spatially periodic modes referred to as persistent spin helix (PSH) and reflecting the underlying SU (2) symmetry in this case. 10The PSH is robust against all forms of spin-independent scattering. This favorable situation where spin relaxation is suppressed while the spin degree of freedom is still susceptible to electric...

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire, and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.

A geometric phase of electron spin is studied in arrays of InAlAs/InGaAs two-dimensional electron gas rings. By increasing the radius of the rings, the time-reversal symmetric Aharonov-Casher oscillations of the electrical resistance are shifted towards weaker spin-orbit interaction regions with their shortened period. We conclude that the shift is due to a modulation of the spin geometric phase, the maximum modulation of which is approximately 1.5 rad. We further show that the Aharonov-Casher oscillations in various radius arrays collapse onto a universal curve if the radius and the strength of Rashba spin-orbit interaction are taken into account. The result is interpreted as the observation of the effective spin-dependent flux through a ring.

The spin-orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III-V zinc-blende semiconductor heterostructures, two types of spin-orbit interaction--Rashba and Dresselhaus--act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients α and β, respectively. When α is equal to β, the so-called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin rotations is achieved even in the presence of the spin-orbit interaction, implying strongly enhanced spin lifetimes for spatially periodic spin modes. Existing methods to evaluate α/β require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter-free technique to determine α/β and to deduce the absolute values of α and β. The method is based on the detection of the effective magnetic field direction and the strength induced by the two spin-orbit interactions. Moreover, we observe the persistent spin helix symmetry by gate tuning.